MIMO wireless systems are known to provide considerable gains in data rates and diversity advantage over single antenna systems. Effective decoders are needed for multi-antenna systems that operate at these high data rates. Taking full advantage of the optimal performance in MIMO systems usually requires the use of a maximum-likelihood (ML) decoding. However, the complexity of the optimum ML decoder grows exponentially with the number of transmit antennas and the symbol constellation size. Accordingly, there has been a need for decoders that achieve a reasonable trade-off between complexity and performance.
Some of the decoders that tried to achieve this trade-off attempt to modify an initial estimate of a transmit symbol vector, for example in space-time chase decoding and list-sphere decoding. The space-time chasing decoding is described, e.g., in D. J. Love, S. Hosur, A. Batra and R. W. Heath, “Space-time chase decoding,” IEEE Trans. on Wireless Comm., 4(5):2035-2039, 2005 (Love et al.), and the list-sphere decoding is described, e.g., in B. Hochwald and S. T. Brink, “Achieving near-capacity on a multiple-antenna channel,” IEEE Trans. Comm., 51:389{399, March 2002 (Hochwald et al.) and in B. Hassibi and B. Hochwald, “High rate codes that are linear in space and time,” IEEE Transactions on Information Theory, 48(7):1804-1824, July 2002 (Hassibi et al.). These references are incorporated herein by reference in its entirety for all purposes. These decoders may be considered as performing some sort of post-processing on a filtered received symbol vector.
In space-time chase decoding in Love et al., it was shown that there is an improvement in performance of a zero-forcing (ZF) decoder with the addition of space-time chase decoding techniques. A list sphere decoder (LSD) in Hochwald et al. and/or Hassibi et al. attempts to search for the ML estimate by considering only transmit symbol vectors that are within a radius from a ZF estimate. The limitations and drawbacks of the LSD are based on the aspect that the performance is dependent on the search radius. Moreover, it may not be considered in a multiuser scenario.
Accordingly, there is a need for new decoders, decoding methods, and apparatuses and systems using the same.